\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t45\_gfacirc1 (TMS4V2tzMPV6rnZdE9PS1TvjYqn58Mp9geN)}
\maketitle
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_twoscomp : {\iota}$ be given.
Let $ k2\_twoscomp : {\iota}$ be given.
Let $ k3\_gfacirc1 : {\iota}$ be given.
Let $ k2\_msafree2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k19\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_msafree2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_circcomb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_circcomb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k17\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k11\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k6\_margrel1 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k25\_twoscomp : {\iota}$ be given.
Let $ v3\_circcomb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)){\unicdbdjdcd}((r1\_circcomb~X0~X1){\unicdbdjdcd}(\\
k2\_msafree2~(k2\_circcomb~X0~X1)=k2\_xboole\_0~(k4\_xboole\_0~(k2\_msafree2~\\
X0)~(k3\_msafree2~X1))~(k4\_xboole\_0~(k2\_msafree2~X1)~(k3\_msafree2~\\
X0)))))\end{array}
\label{hyp:ehfdpfdgjgchdgdgngcgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_circcomb~X0){\unicdcdcdhd}((v2\_circcomb~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_circcomb~\\
X1){\unicdcdcdhd}((v2\_circcomb~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)))){\unicdbdjdcd}(r1\_circcomb~X0~X1))\end{array}
\label{hyp:ehedhdpfdgjgchdgdgpgngcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \preoh (X0{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~\\
X1~X2)~k3\_twoscomp){\unicdcdcdhd}((X1{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~X2~X0)~k2\_twoscomp){\unicdcdcdhd}\\
((X2{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~X0~X1)~k3\_gfacirc1){\unicdcdcdhd}(k2\_msafree2~\\
(k17\_gfacirc1~X0~X1~X2){\unicdcdgdad}k1\_enumset1~X0~X1~X2)))\end{array}
\label{hyp:ehededpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~\\
X1))){\unicdbdjdcd}((k2\_msafree2~(k5\_circcomb~X0~X1)=k10\_xtuple\_0~X1){\unicdcdcdhd}(k3\_msafree2~\\
(k5\_circcomb~X0~X1)=k1\_tarski~(k4\_tarski~X1~X0)))\end{array}
\label{hyp:ehedcdpfdgjgchdgdgpgngcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k3\_msafree2~(k17\_gfacirc1~X0~\\
X1~X2)=k1\_enumset1~(k4\_tarski~(k10\_finseq\_1~X0~X1)~k3\_gfacirc1)~\\
(k4\_tarski~(k10\_finseq\_1~X1~X2)~k3\_twoscomp)~(k4\_tarski~(k10\_finseq\_1~\\
X2~X0)~k2\_twoscomp)\end{array}
\label{hyp:ehedbdpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (k4\_xboole\_0~X0~X1=k1\_xboole\_0){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddhdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{{k2\_xboole\_0}~{X0}}~{k1\_xboole\_0}}={X0}}}\label{hyp:ehbdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k10\_xtuple\_0~(k11\_finseq\_1~\\
X0~X1~X2)=k1\_enumset1~X0~X1~X2\end{array}
\label{hyp:ehbdcdidpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{X0}}~{X0}}}}\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k6\_subset\_1}~{X0}}~{X1}}={{{k4\_xboole\_0}~{X0}}~{X1}}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~(k4\_finseq\_2~np\_\_2~\\
k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k4\_finseq\_2~np\_\_2~k6\_margrel1)~k6\_margrel1))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k4\_finseq\_2~np\_\_2~k6\_margrel1)~\\
k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_finseq\_2~\\
np\_\_2~k6\_margrel1)~k6\_margrel1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k4\_finseq\_2~np\_\_2~k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_finseq\_2~np\_\_2~\\
k6\_margrel1)~k6\_margrel1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}\\
((v1\_funct\_2~X3~(k4\_finseq\_2~np\_\_3~k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_finseq\_2~np\_\_3~\\
k6\_margrel1)~k6\_margrel1))))){\unicdbdjdcd}({\unicdcdadad} X4 .  {\unicdcdadad} X5 .  {\unicdcdadad} X6 .  \\
k6\_subset\_1~(k1\_enumset1~X4~X5~X6)~(k1\_tarski~(k4\_tarski~(k11\_finseq\_1~\\
(k4\_tarski~(k10\_finseq\_1~X4~X5)~X0)~(k4\_tarski~(k10\_finseq\_1~X5~\\
X6)~X1)~(k4\_tarski~(k10\_finseq\_1~X6~X4)~X2))~X3))=k1\_enumset1~X4~\\
X5~X6))))\end{array}
\label{hyp:mgbdfdpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (v1\_relat\_1~(k11\_finseq\_1~X0~\\
X1~X2)){\unicdcdcdhd}(v1\_funct\_1~(k11\_finseq\_1~X0~X1~X2))\end{array}
\label{hyp:ggdgjdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~\\
X1))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k5\_circcomb~X0~X1)){\unicdcdcdhd}((\preoh v11\_struct\_0~(\\
k5\_circcomb~X0~X1)){\unicdcdcdhd}(v1\_msualg\_1~(k5\_circcomb~X0~X1))))\end{array}
\label{hyp:ggdgjdpfdgjgchdgdgpgngcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  v1\_finseq\_1~(k11\_finseq\_1~X0~\\
X1~X2)\end{array}
\label{hyp:ggdgbdbdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~\\
X1))){\unicdbdjdcd}((\preoh v11\_struct\_0~(k5\_circcomb~X0~X1)){\unicdcdcdhd}((v1\_msualg\_1~(k5\_circcomb~\\
X0~X1)){\unicdcdcdhd}((v1\_circcomb~(k5\_circcomb~X0~X1)){\unicdcdcdhd}(v2\_circcomb~(k5\_circcomb~\\
X0~X1)))))\end{array}
\label{hyp:ggdgbdadpfdgjgchdgdgpgngcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~\\
X1))){\unicdbdjdcd}((\preoh v11\_struct\_0~(k5\_circcomb~X0~X1)){\unicdcdcdhd}((v1\_msualg\_1~(k5\_circcomb~\\
X0~X1)){\unicdcdcdhd}(l1\_msualg\_1~(k5\_circcomb~X0~X1))))\end{array}
\label{hyp:egehpflgfdpfdgjgchdgdgpgngcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k3\_twoscomp){\unicdcdcdhd}((v1\_funct\_2~k3\_twoscomp~(k4\_finseq\_2~\\
np\_\_2~k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~k3\_twoscomp~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k4\_finseq\_2~np\_\_2~k6\_margrel1)~k6\_margrel1))))\end{array}
\label{hyp:egehpflgddpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k3\_gfacirc1){\unicdcdcdhd}((v1\_funct\_2~k3\_gfacirc1~(k4\_finseq\_2~\\
np\_\_2~k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~k3\_gfacirc1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k4\_finseq\_2~np\_\_2~k6\_margrel1)~k6\_margrel1))))\end{array}
\label{hyp:egehpflgddpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k2\_twoscomp){\unicdcdcdhd}((v1\_funct\_2~k2\_twoscomp~(k4\_finseq\_2~\\
np\_\_2~k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~k2\_twoscomp~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k4\_finseq\_2~np\_\_2~k6\_margrel1)~k6\_margrel1))))\end{array}
\label{hyp:egehpflgcdpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k25\_twoscomp){\unicdcdcdhd}((v1\_funct\_2~k25\_twoscomp~(k4\_finseq\_2~\\
np\_\_3~k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~k25\_twoscomp~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_finseq\_2~np\_\_3~k6\_margrel1)~k6\_margrel1))))\end{array}
\label{hyp:egehpflgcdfdpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (\preoh v2\_struct\_0~(k17\_gfacirc1~\\
X0~X1~X2)){\unicdcdcdhd}((\preoh v11\_struct\_0~(k17\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((v1\_msualg\_1~\\
(k17\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((v1\_circcomb~(k17\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}\\
((v2\_circcomb~(k17\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((v3\_circcomb~(k17\_gfacirc1~\\
X0~X1~X2)){\unicdcdcdhd}(l1\_msualg\_1~(k17\_gfacirc1~X0~X1~X2)))))))\end{array}
\label{hyp:egehpflgbdhdpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k4\_tarski~X0~X1=k2\_tarski~(k2\_tarski~X0~\\
X1)~(k1\_tarski~X0)\end{array}
\label{hyp:egfdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k19\_gfacirc1~X0~X1~X2=k2\_circcomb~\\
(k17\_gfacirc1~X0~X1~X2)~(k5\_circcomb~k25\_twoscomp~(k11\_finseq\_1~\\
(k4\_tarski~(k10\_finseq\_1~X0~X1)~k3\_gfacirc1)~(k4\_tarski~(k10\_finseq\_1~\\
X1~X2)~k3\_twoscomp)~(k4\_tarski~(k10\_finseq\_1~X2~X0)~k2\_twoscomp)))\end{array}
\label{hyp:egbdjdpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k17\_gfacirc1~X0~X1~X2=k2\_circcomb~\\
(k2\_circcomb~(k5\_circcomb~k3\_gfacirc1~(k10\_finseq\_1~X0~X1))~(\\
k5\_circcomb~k3\_twoscomp~(k10\_finseq\_1~X1~X2)))~(k5\_circcomb~k2\_twoscomp~\\
(k10\_finseq\_1~X2~X0))\end{array}
\label{hyp:egbdhdpfhgggbgdgjgchdgbd}
\end{equation}
\begin{theorem}\label{thm:ehedfdpfhgggbgdgjgchdgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \preoh (X0{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~\\
X1~X2)~k3\_twoscomp){\unicdcdcdhd}((X1{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~X2~X0)~k2\_twoscomp){\unicdcdcdhd}\\
((X2{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~X0~X1)~k3\_gfacirc1){\unicdcdcdhd}(k2\_msafree2~\\
(k19\_gfacirc1~X0~X1~X2){\unicdcdgdad}k1\_enumset1~X0~X1~X2)))\end{array}$$
\end{theorem}
\end{document}
